Sum of first n natural numbers

Q. Find the arithmetic mean of 17 and 19.

1. 17.5
2. 18
3. 18.5
4. None of these

Q. The digits of a positive three-digit integer are in AP and their sum is 21. The number obtained by reversing the digits is 396 less than the original number. Find the number.

1. 795
2. 579
3. 975
4. None of the above

Q.

How many terms of an AP 27, 24, 21, ... are required to get the sum as 0?

1. 27

2. 19

3. 17

4. 24

Q.

In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back up the next flag and continues the same way until all the flags are on the pole. The total distance covered is

1. 740 m

2. 860 m

3. 820 m

4. 760 m

Q.

A staircase consists of 20 steps. The length and breadth of each step is 100 $m$ and $\frac{1}{2}m$ respectively. The height of the lowermost step is $\frac{1}{2}m$ and the height of the subsequent step increases by $\frac{1}{2}m$. Find the volume in $m^3$ of the concrete required to make the staircase.

1. 5250

2. 2520

3. 5225

4. 5520

Q. The sum of the series
${45}^2-{43}^2+{44}^2-{42}^2+{43}^2-{41}^2+{42}^2-{40}^2+\cdots \text{15 terms}$ is ___.

1. 1650
2. 2220
3. 1290
4. 1900